The European Physical Journal D

, Volume 61, Issue 2, pp 443–448 | Cite as

Counting limit cycles with the help of the renormalization group

  • D. Das
  • D. Banerjee
  • J. K. Bhattacharjee
  • A. K. Mallik
Article

Abstract.

We use the renormalization group to set up an easy algorithm for finding the amplitude equation for an arbitrary two dimensional dynamical system of the Liénard type. This allows us to address the second part of Hilbert’s sixteenth problem, at least in the weak damping limit.

Keywords

Renormalization Group Stable Limit Cycle Amplitude Equation Divergent Term Dimensional Dynamical System 

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Copyright information

© EDP Sciences, SIF, Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • D. Das
    • 1
  • D. Banerjee
    • 2
  • J. K. Bhattacharjee
    • 3
  • A. K. Mallik
    • 3
  1. 1.Department of MathematicsSouth Point High SchoolKolkataIndia
  2. 2.Department of PhysicsJadavpur UniversityKolkataIndia
  3. 3.S.N. Bose National Centre for Basic SciencesKolkataIndia

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